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When Is a Discrete Diffusion a Scale-Space?

Ramunas Girdziusas, Jorma Laaksonen
ICCV 2007 pp. 1-6
doi:10.1109/ICCV.2007.4408895 /iccv/2007/girdziusas2007iccv-discrete/

Abstract

Necessary and sufficient conditions are discussed which state when the Euler-inspired forward diffusion in a discrete space-time is a scale-space in the sense of both the total and sign variation diminishing. We emphasize that the problem is algebraic and reduces to characterization of the elements of the generalized Laplacian so that the diffusion propagators are positive definite. As a key-product, explicit analytical expressions are found for the principal minors of the frequently-applied class of tridiagonal (Jacobi) matrices. Further generalizations are outlined by introducing novel techniques of evaluating matrix determinants.

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Cite

Text

Girdziusas and Laaksonen. "When Is a Discrete Diffusion a Scale-Space?." IEEE/CVF International Conference on Computer Vision, 2007. doi:10.1109/ICCV.2007.4408895

Markdown

[Girdziusas and Laaksonen. "When Is a Discrete Diffusion a Scale-Space?." IEEE/CVF International Conference on Computer Vision, 2007.](https://mlanthology.org/iccv/2007/girdziusas2007iccv-discrete/) doi:10.1109/ICCV.2007.4408895

BibTeX

@inproceedings{girdziusas2007iccv-discrete,
  title     = {{When Is a Discrete Diffusion a Scale-Space?}},
  author    = {Girdziusas, Ramunas and Laaksonen, Jorma},
  booktitle = {IEEE/CVF International Conference on Computer Vision},
  year      = {2007},
  pages     = {1-6},
  doi       = {10.1109/ICCV.2007.4408895},
  url       = {https://mlanthology.org/iccv/2007/girdziusas2007iccv-discrete/}
}